Homotopy Type Theory category theory > history (Rev #11)

Here we collect articles about doing category theory in HoTT. This is based off of the HoTT Book.

Definitions

• precategory
• isomorphism?
• category
• functor
• natural transformation
• functor precategory
• left adjoint
• equivalence of precategories
• faithful functor
• full functor
• split essentially surjective
• essentially surjective
• weak equivalence of precategories
• isomorphism of precategories?
• opposite precategory
• product precategory
• hom functor

Theorems

• Rezk completion
• Yoneda lemma

References

• HoTT Book
• Univalent categories and the Rezk completion by Benedikt Ahrens, Chris Kapulkin, Michael Shulman.